How do I update my phone without it asking me to delete more apps but I deleted almost 10 apps

Try connecting the phone to an Mac or PC and try updating that way.

Update software on iPhone, iPad, or iPod touch in iTunes on PCAppleOfficial Apple Support › guide › itunes › windows

Update software on your iPhone, iPad, or iPod touchAppleOfficial Apple Support › guide › mac-help › mac

armani286 Said:

"How do I update my phone without it asking me to delete more apps but I deleted almost 10 apps

It’s saying I need to delete more apps but I deleted almost 10 apps"

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Deleting Apps to Update an iPhone:

Deleting Apps doesn't seems accurate here. Seems you need to clear space, if any clearing at all. So, cleat the following...

Troubleshooting iPhone Storage:

Internal storage cannot be upgraded. It is what it is. So, the maximum internal storage capacity never increases, even if you upgraded your iCloud plan. Learn More here: What's the Difference Between Device Storage and iCloud Storage? Apple Support

So, what to do...

Clear Space Using my User Tips:

• How to Clear Space from your Mobile Device, and What to Clear: - User Tip. You may have too much installed, and need to clear space. So, see my user tip: 
• How to Clear "Other" in your iPhone's Storage - Use Backup - User Tip. Caches would be being used for remembrance of application use. It is essentially the same for an iPhone. You'd backup your iPhone, and then restore your iPhone from the backup you've just created. All System Data will delet